LOS ANGELES — Their team batting average is still a scorching week shy of the Mendoza Line. They have scored runs in precisely five of their last 40 innings. They have worn a path in the grass between the batter’s box and their dugout from all the strikeouts they have piled up. They are at the point where a four-run output, such as the one they mustered Tuesday night, is considered an explosion of offense.

And yet, the St. Louis Cardinals, flaws and all, will wake up Wednesday morning one win away from the World Series. In a 4-2 victory over the Los Angeles Dodgers on Tuesday night at Dodger Stadium in Game 4 of the National League Championship Series, they doubled their run total for the series and put some welcomed distance between themselves and their uncharacteristic sloppy performance of the night before.

But despite the Cardinals’ three-games-to-one lead in the series, there is much work to be done. The Cardinals will face Zack Greinke, the Dodgers’ right-handed ace, in Wednesday’s Game 5, and if they lose that one, Clayton Kershaw, the left-handed ace, awaits them in Game 6 in St. Louis on Friday night. A year ago, the Cardinals held the same 3-1 lead over the San Francisco Giants through four games, only to lose the next three.

“This team that we’re playing against,” Cardinals left fielder Matt Holliday said, “is way too good [for us] to think for some reason it’s not going to be a very tough task to get one more win.”

Holliday and Shane Robinson provided the bulk of the Cardinals’ offense via home runs — the former a towering blast to left by a trusted power source, the latter a wall-scraper by the sort of October hero only the Cardinals could produce.

Holliday’s moonshot “was screaming the whole two minutes it was in the air,” said Robinson, a 5-foot-9 outfielder with five career big league homers in 221 regular season games. “I hit them that way sometimes,” he deadpanned. “But not today.”

The Cardinals’ bullpen, chock-full of flamethrowing youngsters, inherited a slim lead Tuesday night from starter Lance Lynn and brought it home with authority. Seth Maness coaxed a double-play to end the sixth — with shortstop Pete Kozma, who had just entered as a defensive replacement, making a fine play to start it — and phenom Carlos Martinez handled the seventh and eighth. Closer Trevor Rosenthal pitched the ninth for the save. All three Cardinals relievers are rookies.

On the 25th anniversary of Kirk Gibson’s memorable World Series home run in this same ballpark, what passed for late-inning drama for the Dodgers was backup shortstop Nick Punto, after momentarily energizing the crowd with a double to center field in the bottom of the seventh, getting picked off second base — an inexcusable mistake — or right fielder Yasiel Puig, representing the tying run in the bottom of the ninth, grounding into a double play to all but end their final threat.

After pitching had dominated each of the first three games of the series, Tuesday night’s third and fourth innings alone produced more runs than had the previous two games combined. The Cardinals scored three times in the third, on Matt Carpenter’s RBI double and Holliday’s massive homer — the first by either team in this series — which was measured conservatively at 426 feet. The runs were the first for the Cardinals in 14 innings.

The Dodgers got two of the runs back in the fourth, on RBI singles by Puig and A.J. Ellis — with Puig’s single providing one of the more dramatic moments of the night. Three pitches earlier, Lynn had buzzed his chin with a high-and-tight fastball — perhaps a message from the Cardinals regarding Puig’s showboating the night before during a pivotal RBI triple.

Puig shot some death-glares at the mound, but wisely retreated and got back in the batter’s box. Following his emphatic answer, a sharp single up the middle to plate the Dodgers’ first run, Puig gestured joyously to the Dodgers’ dugout but otherwise behaved himself.

More emblematic for the Dodgers on this night, however, was the painful, helpless performance turned in by shortstop Hanley Ramirez, who is attempting to play with a hairline fracture in his rib, and who went 0 for 3 with three strikeouts in his three appearances against Lynn, before the Dodgers finally yanked him. His status for Wednesday is uncertain.

The Cardinals, meanwhile, are a win away from their fourth trip to the World Series in the past decade. When they are at their best, they are relentless, opportunistic and more than a little lucky. They unearth a new, unlikely hero — a David Eckstein, a David Freese, a Pete Kozma, a Shane Robinson — with remarkable regularity.

The Cardinals are hitting just .148 in the NLCS, and have struck out 35 times over these four games, including 11 times on Tuesday night against the soft back-end of the Dodgers’ pitching staff. But all that mattered in Game 4 were those four precious runs, and that third win, and all that matters now is winning one more.

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